Models for Multi-State Survival Data: Rates, Risks, and Pseudo-Values (Chapman & Hall/CRC Texts in Statistical Science)

✍ Scribed by Per Kragh Andersen, Henrik Ravn

• Publisher: CRC
• Year: 2024
• Tongue: English
• Leaves: 293
• Category: Library

✦ Synopsis

Multi-state models provide a statistical framework for studying longitudinal data on subjects when focus is on the occurrence of events that the subjects may experience over time. They find application particularly in biostatistics, medicine, and public health. The book includes mathematical detail which can be skipped by readers more interested in the practical examples. It is aimed at biostatisticians and at readers with an interest in the topic having a more applied background, such as epidemiology. This book builds on several courses the authors have taught on the subject.

Key Features:

• Intensity-based and marginal models
• Survival data, competing risks, illness-death models, recurrent events
• Includes a full chapter on pseudo-values
• Intuitive introductions and mathematical details
• Practical examples of event history data
• Exercises

Software code in R and SAS and the data used in the book can be found on the book’s webpage.

✦ Table of Contents

Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
List of symbols and abbreviations
1. Introduction
1.1. Examples of event history data
1.1.1. PBC3 trial in liver cirrhosis
1.1.2. Guinea-Bissau childhood vaccination study
1.1.3. Testis cancer incidence and maternal parity
1.1.4. PROVA trial in liver cirrhosis
1.1.5. Recurrent episodes in affective disorders
1.1.6. LEADER cardiovascular trial in type 2 diabetes
1.1.7. Bone marrow transplantation in acute leukemia
1.1.8. Copenhagen Holter study
1.2. Parameters in multi-state models
1.2.1. Choice of time-variable
1.2.2. Marginal parameters
1.2.3. Conditional parameters
1.2.4. Data representation
1.2.5. Target parameter
1.3. Independent censoring and competing risks
1.4. Mathematical definition of parameters ()
1.4.1. Marginal parameters ()
1.4.2. Conditional parameters ()
1.4.3. Counting processes ()
1.5. Exercises
2. Intuition for intensity models
2.1. Models for homogeneous groups
2.1.1. Nelson-Aalen estimator
2.1.2. Piece-wise constant hazards
2.1.3. Significance tests
2.2. Regression models
2.2.1. Multiplicative regression models
2.2.2. Modeling assumptions
2.2.3. Cox versus Poisson models
2.2.4. Additive regression models
2.2.5. Additive versus multiplicative models
2.3. Delayed entry
2.4. Competing risks
2.5. Recurrent events
2.5.1. Recurrent episodes in affective disorders
2.5.2. LEADER cardiovascular trial in type 2 diabetes
2.6. Exercises
3. Intensity models
3.1. Likelihood function ()
3.2. Non-parametric models ()
3.2.1. Nelson-Aalen estimator ()
3.2.2. Inference ()
3.3. Cox regression model ()
3.4. Piece-wise constant hazards ()
3.5. Additive regression models ()
3.6. Examples
3.6.1. PBC3 trial in liver cirrhosis
3.6.2. Guinea-Bissau childhood vaccination study
3.6.3. PROVA trial in liver cirrhosis
3.6.4. Testis cancer incidence and maternal parity
3.7. Time-dependent covariates
3.7.1. Adapted covariates
3.7.2. Non-adapted covariates
3.7.3. Inference
3.7.4. Inference ()
3.7.5. Recurrent episodes in affective disorders
3.7.6. PROVA trial in liver cirrhosis
3.7.7. PBC3 trial in liver cirrhosis
3.7.8. Bone marrow transplantation in acute leukemia
3.7.9. Additional issues
3.8. Models with shared parameters
3.8.1. Duplicated data set
3.8.2. PROVA trial in liver cirrhosis
3.8.3. Bone marrow transplantation in acute leukemia
3.8.4. Joint likelihood ()
3.9. Frailty models
3.9.1. Inference ()
3.9.2. Clustered data
3.9.3. Recurrent events
3.10. Exercises
4. Intuition for marginal models
4.1. Plug-in methods
4.1.1. Two-state model
4.1.2. Competing risks
4.1.3. Illness-death models
4.2. Direct models
4.2.1. Two-state model
4.2.2. Competing risks
4.2.3. Recurrent events
4.3. Marginal hazard models
4.3.1. Clustered data
4.3.2. Recurrent events
4.3.3. Illness-death model
4.4. Independent censoring – revisited
4.4.1. Investigating the censoring distribution
4.4.2. Censoring and covariates – a review
4.4.3. Independent competing risks – a misnomer ()
4.4.4. Semi-competing risks ()
4.5. Exercises
5. Marginal models
5.1. Plug-in for Markov processes ()
5.1.1. Two-state model ()
5.1.2. Competing risks ()
5.1.3. Progressive illness-death model ()
5.1.4. Recurrent events ()
5.1.5. Progressive multi-state models ()
5.2. Plug-in for non-Markov processes ()
5.2.1. State occupation probabilities ()
5.2.2. Transition probabilities ()
5.2.3. Recurrent events ()
5.2.4. Semi-Markov processes ()
5.3. Landmarking
5.3.1. Conditional survival probabilities
5.3.2. Landmark super models
5.3.3. Bone marrow transplantation in acute leukemia
5.3.4. Multi-state landmark models
5.3.5. Estimating equations ()
5.4. Micro-simulation
5.4.1. Simulating multi-state processes
5.4.2. Simulating from an improper distribution
5.4.3. PROVA trial in liver cirrhosis
5.5. Direct regression models
5.5.1. Generalized estimating equations ()
5.5.2. Two-state model ()
5.5.3. Competing risks ()
5.5.4. Recurrent events ()
5.5.5. State occupation probabilities ()
5.6. Marginal hazard models ()
5.6.1. Cox score equations – revisited ()
5.6.2. Multivariate Cox model ()
5.6.3. Clustered data ()
5.6.4. Recurrent events ()
5.6.5. Illness-death model ()
5.7. Goodness-of-fit
5.7.1. Cumulative residuals ()
5.7.2. Generalized estimating equations ()
5.7.3. Cox model ()
5.7.4. Direct regression models ()
5.8. Examples
5.8.1. Non-Markov transition probabilities
5.8.2. Direct binomial regression
5.8.3. Extended models for recurrent events
5.8.4. Goodness-of-fit based on cumulative residuals
5.9. Exercises
6. Pseudo-values
6.1. Intuition
6.1.1. Introduction
6.1.2. Hazard difference
6.1.3. Restricted mean
6.1.4. Cumulative incidence
6.1.5. Cause-specific time lost
6.1.6. Non-Markov transition probabilities
6.1.7. Recurrent events
6.1.8. Covariate-dependent censoring
6.2. Theoretical properties ()
6.3. Approximation of pseudo-values ()
6.4. Goodness-of-fit ()
6.5. Exercises
7. Further topics
7.1. Interval-censoring
7.1.1. Markov processes ()
7.1.2. Two-state model ()
7.1.3. Competing risks ()
7.1.4. Progressive illness-death model ()
7.2. Models for dependent data
7.2.1. Times of entry into states
7.2.2. Shared frailty model – two-stage estimation ()
7.3. Causal inference
7.3.1. Definition of causality
7.3.2. The g-formula ()
7.3.3. Inverse probability of treatment weighting ()
7.3.4. Summary and discussion
7.4. Joint models with time-dependent covariates
7.4.1. Random effects model
7.4.2. Likelihood ()
7.4.3. Prediction of survival probabilities
7.4.4. Landmarking and joint models
7.5. Cohort sampling
7.5.1. Nested case-control studies ()
7.5.2. Case-cohort studies ()
7.5.3. Discussion
Bibliography
Subject Index